In fact it may be due to a lack of precision of the Z-buffer : when the farPlane value is too far the precision is reduced, thus leading to some mistakes in rendering. Is 3000 really too high for a back-clip distance ?
Well, yes, but only when your nodes are very close, my test case will be sort of "general", objects will be far from each other, and another thing is - I have triyed to make farPlane of relatively little distance (200), and nearPlane of (1) - didn't help.
BTW, nearPlane distance - would be something to worry about first of all, since depth buffer resolution is much more sensitive to it than to farPlane.
Don't make nearPlane too close...
But anyhow, it doesn't seems to be the depth test problem...
Edit: What about 3000, well... sounds a bit too big, do you realy need it to be so big? Always try to make farPlane as close as your scenario allows, and nearPlane - as far as it is acceptable (1 or 0.5 should be fine, don't do 0.001 etc, as people tend to do)...